The real sequence is indexed from 0 and has the explicit rule a_n=(-3)+(-1)n for n∈N={0,1,2,…}. Find the term at n=9.
G001 — The real sequence is indexed from 0 and has the explicit rule a_n=(-3)+(-1)n for n∈N={0,1,2,…}. Find the term at n=9.
Definition and scope
Use the original question domain, assumptions and cited MKO definitions. This item has second-context mathematical and bilingual review, with the model, answer and every arithmetic step independently recomputed from the original parameters; the source question remains a candidate.
source roles = [qf-sequence-explicit-term, [d, n, operation, u]]
After
derived = [explicit_term, no-invented-domain]
Conditions: none
Keep EACH bank’s keys/operation/domain distinct:LDL/PULSE/function legacy table underscores,TREE full tree_* with its declared domain,and permissive BASE signed without invented op/domain.All arithmetic respects the binary-primitive contract.
Type ALL RAW u/d/count fields EVEN for prefix L=0.Indices start at0 and the formula/recurrence is GIVEN;do not infer a general rule from finite samples.
Sequence ORIGINAL zero-based n times common difference := mul(9, -1)
After
Sequence ORIGINAL zero-based n times common difference = -9
Conditions: none
Use ORIGINAL operands exactly;mul/sub/div have EXPLICITLY TWO operands so the old binary primitive cannot ignore a third.Keep RAW SAFE bounds separate from unbounded derived BigInts;do not approximate to force answers.
Sequence ORIGINAL initial plus n common differences := sum(-3, -9)
After
Sequence ORIGINAL initial plus n common differences = -12
Conditions: none
Use ORIGINAL operands exactly;mul/sub/div have EXPLICITLY TWO operands so the old binary primitive cannot ignore a third.Keep RAW SAFE bounds separate from unbounded derived BigInts;do not approximate to force answers.
S005 · premise_and_result_audit — Reverse-audit THIS question’s ORIGINAL data,types,roles,complete premises and field order.Do not invert implication or turn finite-table checks into infinite-domain/formal proof.Original Q/English/MKO/AST/status remain unchanged.
S004 · premise_and_result_audit — Recompute Sequence ORIGINAL initial plus n common differences with exact rational arithmetic, not rounded decimals.
S003 · premise_and_result_audit — Recompute Sequence ORIGINAL zero-based n times common difference with exact rational arithmetic, not rounded decimals.
S002 · premise_and_result_audit — Reverse-audit THIS question’s ORIGINAL data,types,roles,complete premises and field order.Do not invert implication or turn finite-table checks into infinite-domain/formal proof.Original Q/English/MKO/AST/status remain unchanged.
S001 · premise_and_result_audit — Reverse-audit THIS question’s ORIGINAL data,types,roles,complete premises and field order.Do not invert implication or turn finite-table checks into infinite-domain/formal proof.Original Q/English/MKO/AST/status remain unchanged.
Result
-12
The full substitutions and premise checks give the original answer; source identity,format and status are unchanged.
This question review and source binding
Review date: 2026-10-26
Original questions, answers, step expressions, numeric ASTs and historical records are retained. Source candidate labels remain historical and are not overwritten as formal proof.